Methods and apparatus for transmit IQ mismatch calibration

ABSTRACT

A method of pre-compensating for transmitter in-phase (I) and quadrature (Q) mismatch (IQMM) may include sending a signal through an up-converter of a transmit path to provide an up-converted signal, determining the up-converted signal, determining one or more IQMM parameters for the transmit path based on the determined up-converted signal, and determining one or more pre-compensation parameters for the transmit path based on the one or more IQMM parameters for the transmit path. In some embodiments, the up-converted signal may be determined through a receive feedback path. In some embodiments, the up-converted signal may be determined through an envelope detector.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/092,214 filed Nov. 6, 2020 which is incorporated by reference andwhich claims priority to, and the benefit of, U.S. Provisional PatentApplication Ser. No. 63/025,980 titled “Transmitter Frequency-DependentIn-Phase and Quadrature Mismatch Calibration” filed May 15, 2020 whichis incorporated by reference.

TECHNICAL FIELD

This disclosure relates generally to quadrature transmitters, and morespecifically to transmit IQ mismatch calibration.

BACKGROUND

A quadrature transmitter may include an in-phase (I) path and aquadrature (Q) path. Imbalances between the I and Q paths, which may bereferred to as IQ mismatch (IQMM), may degrade the performance of thetransmitter.

The above information disclosed in this Background section is only forenhancement of understanding of the background of the invention andtherefore it may contain information that does not constitute prior art.

SUMMARY

A method of pre-compensating for transmitter in-phase (I) and quadrature(Q) mismatch (IQMM) may include sending a signal through an up-converterof a transmit path to provide an up-converted signal, determining theup-converted signal through a down-converter of a receive feedback path,determining one or more IQMM parameters for the transmit path based onthe determined up-converted signal, and determining one or morepre-compensation parameters for the transmit path based on the one ormore IQMM parameters for the transmit path. Determining one or more IQMMparameters for the transmit path may include solving a system ofequations, a rust one of the equations may include a first component ofthe up-converted signal and a first parameter representing, at least inpart, a desired frequency response of the transmit path, and a secondone of the equations may include a second component of the up-convertedsignal and a second parameter representing, at least in part, afrequency response of the transmit path due to transmit IQMM. The firstone of the equations may further include a third parameter representing,at least in part, a gain and delay for the transmit path. The method mayfurther include determining an IQMM for the receive feedback path byusing a first local oscillator for the transmit path and a second localoscillator for the receive path, and determining one or more IQMMparameters for the transmit path based on the determined up-convertedsignal may include processing the up-converted signal to compensate forthe IQMM in the receive path. A local oscillator for the transmit pathmay have a frequency shift from a local oscillator for the receivefeedback path. The signal may include a first signal at a firstfrequency, the up-converted signal may include a first up-convertedsignal, and the method may further include sending a second signal at asecond frequency through the up-converter of the transmit path toprovide a second up-converted signal, determining the secondup-converted signal through the down-converter of the receive feedbackpath, and determining one or more IQMM parameters for the transmit pathbased on the determined second up-converted signal.

A method of pre-compensating for transmitter in-phase (I) and quadrature(Q) mismatch (IQMM) may include sending a signal through an up-converterof a transmit path to provide an up-converted signal, determining theup-converted signal through an envelope detector, determining one ormore IQMM parameters for the transmit path based on the determinedup-converted signal, and determining one or more pre-compensationparameters for the transmit path based on the one or more IQMMparameters for the transmit path. Determining one or more IQMMparameters for the transmit path may include applying a firstpre-compensation parameter to the transmit path, determining a firstpower of a component of the up-converted signal caused by transmit IQMMthrough the envelope detector based on the first pre-compensationparameter, applying a second pre-compensation parameter to the transmitpath, and determining a second power of a component of the up-convertedsignal caused by transmit IQMM through the envelope detector based onthe second pre-compensation parameter. Determining one or more IQMMparameters for the transmit path may further include selecting one ofthe first pre-compensation parameter or the second pre-compensationparameter based on a lower of the first power and the second power. Themethod may further include applying one or more additionalpre-compensation parameters to the transmit path, and determining one ormore additional powers of one or more components of the up-convertedsignal caused by transmit IQMM through the envelope detector based onthe one or more additional pre-compensation parameters, and determiningone or more IQMM parameters for the transmit path may include selectingone of the first pre-compensation parameter, the second pre-compensationparameter or the one or more additional pre-compensation parametersbased on a lower of the first power, the second power, or the one ormore additional powers. The signal may include a first signal at a firstfrequency, the up-converted signal may include a first up-convertedsignal, and the method may further include sending a second signal at asecond frequency through the up-converter of the transmit path toprovide a second up-converted signal, determining the secondup-converted signal through the envelope detector, and determining oneor more IQMM parameters for the transmit path based on the determinedsecond up-converted signal. The method may further include applyingfirst and second pre-compensation parameters to the transmit path foreach of the first and second signals, and the first and secondup-converted signals may be determined separately based on the first andsecond pre-compensation parameters. Determining one or more IQMMparameters for the transmit path may include solving a system ofequations based on the determined first and second up-converted signals.A first one of the system of equations may include a function, at leastin part, of the first and second pre-compensation parameters. The secondfrequency may be a negative of the first frequency at baseband. Themethod may further include sweeping the first and second frequencies foreach of the first and second pre-compensation parameters, determiningadditional first and second up-converted signals based on sweeping thefirst and second frequencies, and determining one or more IQMMparameters for the transmit path over frequency based on the determinedadditional up-converted signals. The signal may include a first two-tonesignal, the up-converted signal may include a first up-convertedtwo-tone signal, and the method may further include sending a secondtwo-tone signal through the up-converter of the transmit path to providea second up-converted two-tone signal, determining the secondup-converted two-tone signal through the envelope detector, anddetermining one or more IQMM parameters for the transmit path based onthe determined second up-converted two-tone signal. Determining one ormore IQMM parameters for the transmit path may include solving a systemof equations based on the determined first and second up-convertedtwo-tone signals, and at least one of the equations may include a firstparameter of a first frequency of the first two-tone signal and a secondparameter of a second frequency of the first two-tone signal. The methodmay further include sweeping first and second frequencies of at leastone of the two-tone signals, determining additional first and secondup-converted two-tone signals based on sweeping the first and secondfrequencies, and determining one or more IQMM parameters for thetransmit path over frequency based on the determined additionalup-converted two-tone signals.

A system may include an IQ transmit path comprising an up-converter, anenvelope detector arranged to provide an envelope of an up-convertedsignal from the IQ transmit path, a signal generator arranged to apply apilot signal to the IQ transmit path, a signal observer arranged tocapture the envelope of the up-converted signal based on the pilotsignal, and a processor configured to: estimate one or more IQ mismatch(IQMM) parameters for the IQ transmit path based on the capturedenvelope of the up-converted signal, and estimate one or morecompensation coefficients for the IQ transmit path based on theestimated IQMM parameters. The signal observer may be arranged tocapture the envelope of the up-converted signal through a branch of anIQ receiver.

A system may include an IQ transmit path comprising an up-converter, anIQ receive path comprising a down-converter, a feedback connectionarranged to couple an up-converted signal from the IQ transmit path tothe IQ receive path, a signal generator arranged to apply a pilot signalto the IQ transmit path, a signal observer arranged to capture theup-converted signal through the IQ receive path based on the pilotsignal, and a processor configured to: estimate one or more IQ mismatch(IQMM) parameters for the IQ transmit path based on the capturedup-converted signal, and estimate one or more compensation coefficientsfor the IQ transmit path based on the estimated IQMM parameters.

BRIEF DESCRIPTION OF THE DRAWINGS

The figures are not necessarily drawn to scale and elements of similarstructures or functions are generally represented by like referencenumerals for illustrative purposes throughout the figures. The figuresare only intended to facilitate the description of the variousembodiments disclosed herein. The figures do not describe every aspectof the teachings disclosed herein and do not limit the scope of theclaims. The accompanying drawings, together with the specification,illustrate example embodiments of the present disclosure, and, togetherwith the description, serve to explain the principles of the presentdisclosure.

FIG. 1 illustrates an example embodiment of an IQ transmitter that maybe used to implement any of the TX IQMM estimation and/or compensationtechniques according to this disclosure.

FIG. 2 illustrates an example embodiment of complex-valuedpre-compensator (CVC) structure for which coefficients may be estimatedaccording to this disclosure.

FIG. 3 illustrates an embodiment of a system that may be used toimplement TX FD-IQMM calibration using an RX feedback path according tothis disclosure.

FIG. 4 illustrates an example embodiment of a system that may be used toimplement TX FD-IQMM calibration using an RX feedback path according tothis disclosure.

FIG. 5 illustrates example embodiments of spectral plots of transmittedand captured (observed) signals corresponding to some equationsaccording to this disclosure.

FIG. 6 illustrates an embodiment of a system that may be used toimplement TX FD-IQMM calibration using an envelope detector according tothis disclosure.

FIG. 7 illustrates an example embodiment of a system that may be used toimplement TX FD-IQMM calibration using an envelope detector according tothis disclosure.

FIG. 8 illustrates some spectral plots of transmitted and captured(observed) signals using a first embodiment of a method for TX IQMMcalibration using an envelope detector according to this disclosure.

FIG. 9 illustrates some spectral plots of transmitted and captured(observed) signals using a third embodiment of a method for TX IQMMcalibration using an envelope detector according to this disclosure.

FIG. 10 illustrates an embodiment of method for TX IQMM calibrationusing an RX feedback path according to this disclosure.

FIG. 11 illustrates an embodiment of a first method for TX IQMMcalibration using an envelope detector according to this disclosure.

FIG. 12 illustrates an embodiment of a second method for TX IQMMcalibration using an envelope detector according to this disclosure.

FIG. 13 illustrates an embodiment of a third method for TX IQMMcalibration using an envelope detector according to this disclosure.

FIG. 14 illustrates an embodiment of a method of pre-compensating fortransmitter IQMM according to this disclosure.

FIG. 15 illustrates another embodiment of a method of pre-compensatingfor transmitter IQMM according to this disclosure.

DETAILED DESCRIPTION Overview

This disclosure encompasses numerous inventive principles relating topre-compensation for in-phase (I) and quadrature (Q) mismatch (IQMM) inquadrature up-conversion transmitters. Pilot signals may be applied atbaseband to a transmit (TX) path, and the IQMM impaired up-convertedsignals may be captured and processed using various disclosed techniquesand algorithms to estimate the TX IQMM, which may include bothfrequency-independent IQMM (FI-IQMM) and frequency-dependent IQMM(FD-IQMM). The estimated IQMM may then be used to determine coefficientsfor a pre-compensator in the TX path.

In some embodiments, the IQMM impaired up-converted signals may becaptured through a receive (RX) feedback path having a quadraturedown-converter. Single-tone pilot signals may be applied at differentfrequencies, and primary and mirror components of the captureddown-converted signals may be used in a system of equations to estimateIQMM parameters for the TX path. Effects of RX IQMM in the RX feedbackpath may be reduced or eliminated through various disclosed techniques,for example, by using separate local oscillators for the TX and RX pathsand/or a frequency shift between the local oscillators for the TX and RXpaths.

In some embodiments, the IQMM impaired up-converted signals may becaptured through an envelope detector and processed using variousdisclosed techniques. In a first method using an envelope detector, asingle-tone pilot signal may be applied while varying one or morepre-compensation parameters. A single-tone pilot signal applied atbaseband may produce a signal at the output of the envelope detectorhaving a component at twice the frequency of the pilot signal if thereis IQMM in the TX path. Thus, the first method may sweep one or morepre-compensation parameters while applying a first single-tone pilotsignal and selecting one or more of the parameters that provide thelowest output power from the envelope detector at twice the frequency ofthe pilot signal. A search may be performed by repeating this process atother frequencies to select one or more parameters for each frequency.The selected parameters may then be used to estimate IQMM parameters forthe TX path.

In a second method using an envelope detector, one or more TX IQMMparameters for a given frequency may be estimated directly by separatelysending the negative and positive frequencies of a single-tone pilotsignal at baseband using two different sets of pre-compensator settings.The components at twice the given frequency at the output of theenvelope detector may be combined in a set of equations and solved forthe frequency-dependent gain and phase mismatch at the given frequency.This process may be repeated to determine the frequency-dependent gainand phase mismatch at other frequencies, which may then be used toestimate the IQMM parameters for the TX path.

In a third method using an envelope detector, various combinations ofthe negative and positive frequencies of two-tone pilot signals may beapplied separately to the TX path at baseband. The outputs of theenvelope detector at various frequencies may be combined and solvedusing a set of equations to obtain estimates of the TX IQMM parametersdirectly.

Once TX IQMM parameters are determined by any of these disclosedtechniques, they may be used to determine coefficients for apre-compensator in the TX path.

The principles disclosed herein may have independent utility and may beembodied individually, and not every embodiment may utilize everyprinciple. Moreover, the principles may also be embodied in variouscombinations, some of which may amplify benefits of the individualprinciples in a synergistic manner.

TX Pre-Compensation

In quadrature up-conversion transmitters. IQMM between the I and Qbranches may create interference between the mirror frequencies afterup-conversion to radio frequency (RF) or intermediate frequency (IF).Thus, the IQMM may degrade system performance by reducing the effectivesignal-to-interference-plus-noise ratio (SINR). Frequency-independentIQMM (FI-IQMM) may originate from imbalances at mixers, whilefrequency-dependent IQMM (FD-IQMM) may be caused by mismatch betweenoverall frequency responses on the I and Q paths. In some embodiments,only frequency-independent IQMM (FI-IQMM) may be compensated. However,in some applications such as wideband systems (e.g., mmWave systems).FI-IQMM compensation alone may not provide adequate performance. Thus,some of the inventive principles of this application relate totechniques for providing FD-IQMM compensation for quadratureup-converter transmitters. Moreover, TX IQMM may be different than RXIQMM. Therefore, in some embodiments, calibration methods for a TX pathaccording to this disclosure may be different than that those for an RXpath.

FIG. 1 illustrates an example embodiment of an IQ transmitter that maybe used to implement any of the TX IQMM estimation and/or compensationtechniques according to this disclosure. The transmitter 100 illustratedin FIG. 1 may include an I signal path including a digital-to-analogconverter (DAC) 104, a low-pass filter 108 having an impulse responseh_(ITX)(t), and a mixer 112. The transmitter 100, which may also bereferred to as a TX path, may also include a Q signal path including aDAC 106, a low-pass filter 110 having an impulse response h_(QTX)(t),and a mixer 114. The mixers 112, 114 and filters 108, 110, along withsumming circuit 116, may collectively form an up-converter. Thetransmitter 100 may further include an IQMM pre-compensator 118.

In the transmitter, g_(TX)≠1 and ϕ_(TX)≠0 may denote the TX gain andphase mismatches, respectively, that may create frequency-independent IQmismatch (FI-IQMM) at the transmitter. The mismatch between the overallfrequency responses h_(ITX)(t) and h_(QTX)(t) in the I and Q paths ofthe TX path may create FD-IQMM in the TX path, that is,h_(ITX)(t)≠h_(QTX)(t).

The baseband equivalent of the upconverted signal in the TX path 100 (atthe output of the mixers) in the frequency-domain may be given byZ _(TX)(f)=G _(1TX)(f)U(f)+G _(2TX)(f)U*(−f),  (1)where U(f) may be the frequency response of the desired baseband (BB)signal at the input of the analog baseband (ABB) filters 108 and 110 inthe TX path, and G_(1TX)(f) and G_(2TX)(f) may be defined as

$\begin{matrix}{{{G_{1{TX}}(f)} = \frac{{H_{ITX}(f)} + {g_{TX}e^{{j\varnothing}_{TX}}{H_{QTX}(f)}}}{2}},{{G_{2{TX}}(f)} = {\frac{{H_{ITX}(f)} - {g_{TX}e^{{j\varnothing}_{TX}}{H_{QTX}(f)}}}{2}.}}} & (2)\end{matrix}$

In Equations (2). H_(ITX)(f) and H_(QTX)(f) may denote the frequencyresponses of filter 108 (h_(ITX)(t)) and filter 110 (h_(QTX)(t)),respectively. In Equation (1), G_(1TX)(f)U(f) may represent a desired TXsignal, and G_(2TX)(f)U*(−f) may represent a TX image signal. Withoutany IQMM, (g_(TX)=1, ϕ_(TX)=0, and h_(1TX)(t)=h_(QTX)(t)), G_(2TX)(f),and consequently, the second term in Equation (1) may become zero. Thus,In some embodiments, G_(1TX)(f) may represent a desired frequencyresponse of the transmit path, and G_(2TX)(f) may represent a frequencyresponse of the transmit path due to IQMM.

In some embodiments according to this disclosure, the effects of IQMM inthe transmitter 100 may be compensated by estimating one or more IQMMparameters in the transmitter, and then using the estimated IQMMparameters to determine pre-compensation parameters.

The one or more IQMM parameters may include any parameters that may beaffected by IQMM in the TX path such as gain mismatch g_(TX), phasemismatch ϕ_(TX), filters h_(ITX)(t) and h_(QTX)(t) (and/or theirfrequency responses H_(ITX)(f) and H_(QTX)(f)), G_(1TX)(f), G_(2TX)(f),V_(TX)(f) (as described below), and/or the like. In some exampleembodiments described below, the parameters ϕ_(TX) and V_(TX)(f) may beused as the IQMM parameters because, for example, they may reduce thecomplexity and/or effort involved with mathematical derivations.However, other IQMM parameters may be used according to this disclosure.For example, in some example embodiments, G_(1TX)(f) and G_(2TX)(f) maybe used as IQMM parameters which may be estimated and then used todetermine pre-compensation parameters.

The pre-compensation parameters may be any parameters that may determinehow the IQMM pre-compensator 118 may affect the IQMM in the TX path 100.An example of pre-compensation parameters may be coefficients for theIQMM pre-compensator 118 (IQMC coefficients) which may shape the BBsignal s[n]=s_(I)[n]+js_(Q)[n] so as to reduce or eliminate an imagecomponent in the upconverted signal z_(TX)(t). Examples of IQMCcoefficients that may be obtained based on estimated IQMM parameters aredescribed below.

In some embodiments, the IQMM parameter V_(TX)(f) mentioned above, whichmay depend on the TX gain and filter mismatches, may be defined asfollows

$\begin{matrix}{{V_{TX}(f)}\overset{\Delta}{=}{\frac{H_{ITX}(f)}{g_{TX}{H_{QTX}(f)}}.}} & (3)\end{matrix}$

Various calibration algorithms described herein may be used to estimatephase mismatch ϕ_(TX) and V_(TX)(f) for continuous-time frequenciesf=±f₁, . . . , ±f_(K) across a desired frequency band. The estimates ofϕ_(TX) and V_(TX)(f) may then be used to obtain IQ mismatch compensator(IQMC) coefficients for the pre-compensator 118 to reduce TX FD-IQMM.

FIG. 2 illustrates an example embodiment of a complex-valuedpre-compensator (CVC) structure for which coefficients may be estimatedaccording to this disclosure. The embodiment illustrated in FIG. 2 mayinclude an integer delay element 200 having a delay T_(D), a complexconjugate block 202, a complex-valued filter 204 having an impulseresponse w_(TX)[n], and a summing circuit 206.

Values for coefficients for the pre-compensator illustrated in FIG. 2 ,which may fully or partially remove TX FD-IQMM from the transmitter 100illustrated in FIG. 1 , may then be given by

$\begin{matrix}{{W_{TX}^{opt}(f)} = {{{- \frac{G_{2{TX}}(f)}{G_{1{TX}}(f)}}e^{{- {j2\pi}}\;{fT}_{D}}} = {\frac{1 - {{V_{TX}(f)}e^{- {j\phi}_{TX}}}}{1 + {{V_{TX}(f)}e^{- {j\phi}_{TX}}}}e^{{- {j2\pi}}\;{fT}_{D}}}}} & (4)\end{matrix}$where W_(TX) ^(opt)(f) may denote the frequency response of filterw_(TX)[n]. From Equation (4), it may be apparent that optimal responsesof IQMC coefficients may involve knowledge of ϕ_(TX) and/or V_(TX)(f),which may be estimated, for example, using any of the techniquesdisclosed herein.

In some embodiments, and depending on the implementation details, themethods, expressions, and/or the like disclosed herein may provideoptimal values, and thus, the designator “opt” may be used. However, theinventive principles are not limited to embodiments in which optimalvalues may be obtained, and the use of “opt” or “optimal” is not limitedto methods, expressions, and/or the like that may provide optimalvalues.

Some example embodiments of the CVC structure illustrated in FIG. 2 mayinclude any of the following implementation details. The complex-valuedfilter 204 having the impulse response w_(TX)[n] may be implemented, forexample, as a finite impulse response (FIR) filter. The complexconjugate block 202 may be configured to output the complex conjugate ofthe signal s[n] as, for example, s[n]*=s_(I)[n]−js_(Q)[n]. The integerdelay element 200 having the delay T_(D) may be configured to create adelay in the input signal as, for example, s[n−T_(D)].

The CVC structure illustrated in FIG. 2 is provided as an example forpurposes of illustrating the inventive principles of this disclosure,but other IQMM pre-compensation structures and/or combinations thereof,may be used. For example, in some embodiments, a real-valued compensator(RVC) architecture may be use.

RX Feedback Path

FIG. 3 illustrates an embodiment of a system that may be used toimplement TX FD-IQMM calibration using an RX feedback path according tothis disclosure. The embodiment illustrated in FIG. 3 may include a TXpath 300, an RX path 302, a feedback connection 304, and a signalprocessing unit 306. The TX path 300 may include a pre-compensator 308,a digital-to-analog converter (DAC) 310, an up-converter 314, and aradio frequency (RF) transmission block 316. The RX path 302 may includean RF reception block 318, a down-converter 320, and ananalog-to-digital converter (ADC) 324. In some embodiments, the RX path302 may further include a compensator (not shown). The signal processingunit 306 may include a signal generator 328, a signal capture unit 330,and a signal processor 332.

The feedback connection 304 may be implemented with any suitableapparatus such as switches, couplers, conductors, transmission lines,filters, and/or the like. The feedback connection 304 may be coupled tothe TX path 300 at any location after the up-converter 314. The feedbackconnection 304 may be coupled to the RX path 302 at any location beforethe down-converter 320. In some embodiments, some or all of the feedbackconnection 304 may be integral with the TX path 300 and/or the RX path302.

The TX path 300 and the RX path 302 may each include an I signal path orbranch and a Q signal path or branch. The RF transmission block 316 mayinclude various components to transmit an RF signal such as a poweramplifier, a band-pass filter, an antenna, and/or the like. The RFreception block 318 may include various components to receive an RFsignal such as an antenna, a band-pass filter, a low noise amplifier(LNA) and/or the like. Depending on whether the system is in anoperational mode or a calibration mode. IQMM in the TX path 300 may becorrected by the IQMM pre-compensator 308.

In some embodiments, the processor 332 may manage and/or control theoverall operation of the system illustrated in FIG. 3 . This may includecontrolling the application of one or more pilot signals to the TX path300, capturing observations of the up-converted pilot signals throughthe RX path 302, performing calculations and/or offloading calculationsto other resources, providing estimated coefficients to the TXpre-compensator 308, controlling the TX pre-compensator 308 duringtransmission and/or sending of pilot signals, for example, by disablingthe pre-compensator 308, placing it in a transparent or pass-throughstate, and/or the like.

Although various components illustrated in FIG. 3 may be shown asindividual components, in some embodiments, multiple components and/ortheir functionality may be combined into a smaller number of components.Likewise, a single component and/or its functionality may be distributedamong, and/or integrated with, other components. For example, the signalgenerator 328 and/or signal capture unit 330 may be integrated with,and/or their functions may be performed by, one or more similarcomponents in a modem that may be coupled to the transceiver shown inFIG. 3 .

The components of the signal processing unit 306 may be implemented withhardware, software, and/or any combination thereof. For example, full orpartial hardware implementations may include combinational logic,sequential logic, timers, counters, registers, gate arrays, amplifiers,synthesizers, multiplexers, modulators, demodulators, filters, vectorprocessors, complex programmable logic devices (CPLDs), fieldprogrammable gate arrays (FPGAs), state machines, data converters suchas ADCs and DACs, and/or the like. Full or partial softwareimplementations may include one or more processor cores, memories,program and/or data storage, and/or the like, which may be locatedlocally and/or remotely, and which may be programmed to executeinstructions to perform one or more functions of the components of thesignal processing unit 306.

FIG. 4 illustrates an example embodiment of a system that may be used toimplement TX FD-IQMM calibration using an RX feedback path according tothis disclosure. The embodiment illustrated in FIG. 4 may include a TXpath 400, an RX path 402, and an RX feedback connection 403. The TX path400, which may be similar to the transmitter 100 illustrated in FIG. 1 ,may include an I signal path including a DAC 404, a low-pass filter 408having an impulse response h_(ITX)(t), and a mixer 412. The TX path 400may also include a Q signal path including a DAC 406, a low-pass filter410 having an impulse response h_(QTX)(t), and a mixer 414. The mixers412 and 414 and filters 408 and 410, along with summing circuit 416, maycollectively form an up-converter. The TX path 400 may further includean IQMM pre-compensator 418.

The RX path 402 may include an I signal path including a mixer 426, alow-pass filter 430 having an impulse response h_(IRX)(t), and an ADC434. The RX path 402 may also include a Q signal path including a mixer428, a low-pass filter 432 having an impulse response h_(QRX)(t), and anADC 436. The mixers 426 and 428 and filters 430 and 432 may collectivelyform a down-converter. In some embodiments, the RX path 402 may furtherinclude an IQMM compensator (not shown) which may be disabled or placedin a pass-through state during a calibration operation.

In some embodiments, during a calibration operation. IQMMpre-compensator 418 may be disabled or placed in a pass-through modesuch that IQMC may be unity, and therefore U(f)=S(f).

To estimate the IQMM parameters ϕ_(TX) and V_(TX)(f), a single-tonesignal may be applied at baseband of the TX path 400 at frequency f_(k),that is, U(f)=A_(TX)δ(f−f_(k)) where A_(TX) may be an unknown scalingfactor that may account for gain and/or delay of the path between the TXbaseband signal generation and the input of the ABB filters 408 and 410.The IQMM impaired up-converted signal may be observed by capturing thefrequency response of the down-converted signal through the RX feedbackpath at the principal and image frequencies (f_(k) and −f_(k)), whichmay be denoted by R_(1,k)

R(f_(k)) and R_(2,k)

R(−f_(k)). Next, a single-tone signal at frequency −f_(k), that is.U′(f)=A*_(TX)δ(f+f_(k)), may be sent through the TX path 400, and thedown-converted signal at frequencies −f_(k) and f_(k) may be denoted byR_(3,k)=R′(−f_(k)) and R_(4,k)=R′(f_(k)), respectively. Collecting allof the observations may provide the following set of equationsR _(1,k) =A _(TX) A _(RX) G _(1TX)(f _(k))R _(2,k) =A* _(TX) A _(RX) G _(2TX)(−f _(k))R _(3,k) =A* _(TX) A _(RX) G _(1TX)(−f _(k))R _(4,k) =A _(TX) A _(RX) G _(2TX)(f _(k))  (5)where A_(RX) may denote the gain and/or delay from the RX ABB filters430 and 432 to the RX BB. In some embodiments, the four Equations (5)may be time-aligned for correct estimation of IQMM parameters.

FIG. 5 illustrates example embodiments of spectral plots of transmittedand captured (observed) signals corresponding to the Equations (5).

The single-tone signal (e.g., f_(k)) may be swept across the channelband for all selected frequencies to obtain estimates of ϕ_(TX) andV_(TX)(f) using Equations (5) as follows

$\begin{matrix}{{{\hat{\phi}}_{TX} = {\frac{1}{2K}{\sum\limits_{k = 1}^{K}{{angle}\left( \frac{T^{*}\left( {- f_{k}} \right)}{T\left( f_{k} \right)} \right)}}}},{{{\hat{V}}_{TX}(f)} = {{T(f)}e^{{+ j}{\hat{\phi}}_{TX}}}},{f = {\pm f_{1}}},\cdots,{\pm f_{K}}} & (6)\end{matrix}$where

$\begin{matrix}{{{T\left( f_{k} \right)} = \frac{R_{1,k} + R_{4,k}}{R_{1,k} - R_{4,k}}},{{T\left( {- f_{k}} \right)} = \frac{R_{3,k} + R_{2,k}}{R_{3,k} - R_{2,k}}},{k = 1},{\cdots\mspace{14mu}{K.}}} & (7)\end{matrix}$

In some implementations of the calibration algorithm described above,the IQMM at the RX feedback path may be assumed to be zero. In someother implementations, the RX feedback path may introduce RX IQMM intothe observations as well, which may degrade the estimation accuracy ofthe TX IQMM parameters.

In some embodiments, either or both of the two techniques describedbelow may reduce or eliminate the effects of IQMM in the RX feedbackpath on observations of up-converted pilot signals according to thisdisclosure.

In a first technique according to this disclosure, RX FD-IQMC may becalibrated using separate local oscillators (LOs) for the TX and RXpaths in loopback mode (e.g., sweeping the TX LO and using a DC tone atBB of the TX path while keeping RX LO fixed). Next, BB TX tones may beswept across frequency keeping both the TX LO and RX LO fixed at thesame frequency. The TX FD-IQMC coefficients may then be determined. Insome embodiments, an additional step may be added to post-process thereceived signal R(f) to remove the effect of RX-IQMM before estimationof ϕ_(TX) and V_(TX)(f).

In a second technique according to this disclosure, a frequency shiftmay be created between the LOs of the TX and RX paths such that theRX-IQMM may not interfere with the principal and mirror signals of theTX path. In some embodiments, the frequency shift between the LOs may bekept relatively small, for example, to preserve the approximate symmetryof the ABB filter response that the TX principal and image signals mayobserve.

Envelope Detector

FIG. 6 illustrates an embodiment of a system that may be used toimplement TX FD-IQMM calibration using an envelope detector according tothis disclosure. The system illustrated in FIG. 6 may include a TX path600 and a signal processing unit 606 that may be constructed and/oroperate in a manner similar to those illustrated in FIG. 3 .Specifically, the TX path 600 may include a pre-compensator 608, adigital-to-analog converter (DAC) 610, an up-converter 614, and a radiofrequency (RF) transmission block 616. The signal processing unit 606may include a signal generator 628, a signal capture unit 630, and asignal processor 632.

The system illustrated in FIG. 6 may further include an envelopedetector 640 and a signal return path 642. The envelope detector 640,which may be implemented using any suitable apparatus including diodes,filters, and/or the like, may be coupled to the TX path 600 at anylocation after the up-converter 614. The return signal path 642 mayinclude any suitable apparatus such as switches, couplers, conductors,transmission lines, filters, data converters, and/or the like.

In some embodiments, the envelope detector 640 may provide an outputhaving a form, for example, of y(t)=|z(t)|². In some embodiments, someor all of the envelope detector 640 may be integral with the TX path600.

In some embodiments, the 640 envelope detector may output the envelopeof the IQMM impaired up-converted signal and feed it back to the signalprocessing unit 606 without going through a mixer. Thus, the capturedsignal may only contain TX IQMM without any RX impairments. Although thereturn signal path 642 is not limited to any specific implementationdetails, in some embodiments, either the I or Q signal path downstreamof a multiplier in a quadrature receiver may be used as the returnsignal path. This may be convenient, for example, in a transceiversystem in which the RX path already exists.

FIG. 7 illustrates an example embodiment of a system that may be used toimplement TX FD-IQMM calibration using an envelope detector according tothis disclosure. The system illustrated in FIG. 7 may include a TX path700, an RX path 702, and an envelope detector 740.

The TX path 700, which may be similar to the TX path 400 illustrated inFIG. 4 , may include an I signal path including a DAC 704, a low-passfilter 708 having an impulse response h_(ITX)(t), and a mixer 712. TheTX path 700 may also include a Q signal path including a DAC 706, alow-pass filter 710 having an impulse response h_(QTX)(t), and a mixer714. The mixers 712 and 714 and filters 708 and 710, along with summingcircuit 716, may collectively form an up-converter. The TX path 700 mayfurther include an IQMM pre-compensator 718.

The RX path 702, which may be similar to the RX path 402 illustrated inFIG. 4 , may include an I signal path including a mixer 726, a low-passfilter 730 having an impulse response h_(IRX)(t), and an ADC 734. The RXpath 702 may also include a Q signal path including a mixer 728, alow-pass filter 732 having an impulse response h_(QRX)(t), and an ADC736. The mixers 726 and 728 and filters 730 and 732 may collectivelyform a down-converter. In some embodiments, the RX path 702 may furtherinclude an IQMM compensator which may be disabled or placed in apass-through state during a calibration operation.

The envelope detector 740 may be connected to the TX path 700 at anylocation after the up-conversion unit. It may also be connected to theRX path 702 at any location after the mixers 726 and 728. In theembodiment illustrated in FIG. 7 , the envelope detector 740 isconnected to the I path of the RX path, but it may be connected to the Qside as well.

Embodiments of three different methods of estimating TX IQMM using anenvelope detector are described below in the context of the exampleembodiment illustrated in FIG. 7 . These methods, however, are notlimited to these or any other system implementation details.

Method 1

In some embodiments, this method may seek to obtain single-tappre-compensator filter coefficients that may cancel IQMM atfrequencies±f₁, . . . , ±f_(K). These coefficients may then be used toestimate IQMM parameters ϕ_(TX) and V_(TX)(f).

Referring to FIG. 8 , in some embodiments, a single-tone signal atfrequency −f_(k) sent at baseband may produce an output at the envelopedetector having a component at frequency 2f_(k) if there is any IQMM inthe TX chain. Therefore, single-tap pre-compensator coefficients (insome implementations, the best or optimal coefficients) for frequencyf_(k) may be found by sending a single-tone signal from baseband of TXat frequency −f_(k), sweeping pre-compensator coefficients (in someimplementations one tap may be adequate) and choosing the coefficientsthat may provide the lowest power at the output of the envelope detectorat twice the frequency of the BB signal. i.e., 2f_(k). For a single-tonesignal sent at frequency −f_(k), the output of the envelope detectorpath may be denoted by r(t), and its response (ignoring higher frequencycomponents) may be given by:

$\begin{matrix}{{r(t)} = {{{{Re}\left\{ {{z_{TX}(t)}e^{j\;\omega_{{LO}_{TX}}t}} \right\}}}^{2} = {{{A_{TX}{G_{1{TX}}\left( {- f_{k}} \right)}}}^{2} + {{A_{TX}^{*}{G_{2{TX}}\left( f_{k} \right)}}}^{2} + {2{Re}{\left\{ {A_{TX}^{2}{G_{1{TX}}^{*}\left( {- f_{k}} \right)}{G_{2{TX}}\left( f_{k} \right)}e^{{- j}\; 2{\pi 2}\; f_{k}t}} \right\}.}}}}} & (8)\end{matrix}$

The frequency response of the envelope detector output at frequency2f_(k) may be given byR(f)|_(f=2) fk=A _(TX) ² G* _(1TX)(−f _(k))G _(2TX)(f _(k)).  (9)

In the absence of IQMM, G_(2TX)(f_(k)) may be zero and thus R(2f_(k)) inEquation (9) may become zero. By performing a search of pre-compensatorcoefficients, one-tap pre-compensator settings. i.e.,w_(TX)[n]=w_(TX,0)×δ[n], may be obtained such that R(2f_(k)) may becomezero and cancel IQMM at frequency f_(k). After sweeping f_(k) andobtaining the IQMC coefficients (e.g., optimal coefficients) over allfrequency tones denoted by w_(TX,0) ^(opt)(f) for T_(D)=0, then ϕ_(TX)and V_(TX)(f) may be estimated as follows for a CVC structure

$\begin{matrix}{{{\hat{\phi}}_{TX} = {\frac{1}{2K}{\sum\limits_{k = 1}^{K}\;{{angle}\left( {\frac{1 + {w_{{TX},0}^{opt}\left( f_{k} \right)}}{1 + {w_{{TX},0}^{{opt}*}\left( {- f_{k}} \right)}} \times \frac{1 - {w_{{TX},0}^{{opt}*}\left( {- f_{k}} \right)}}{1 - {w_{{TX},0}^{opt}\left( f_{k} \right)}}} \right)}}}},{{{\hat{V}}_{TX}(f)} = {\frac{1 - {w_{{TX},0}^{opt}(f)}}{1 + {w_{{TX},0}^{opt}(f)}}e^{j\;{\hat{\phi}}_{TX}}}},{f = {\pm f_{1}}},\cdots\;,{\pm {f_{K}.}}} & (10)\end{matrix}$

In some embodiments, a search of pre-compensator coefficients may beimplemented as an extensive or exhaustive search. For example, a searchmay be conducted over a wide range of pre-compensator settings and/orfrequency tones at fixed intervals. In some embodiments, a search may beperformed in stages. For example, an initial search may be conducted ona relatively coarse grid of pre-compensator settings and/or frequencytones over a wide range at wider intervals. One or more additionalsearches may then be performed on a finer grid at smaller intervals overone or more smaller ranges based on the results of the coarse search.

Method 2

In some embodiments, this method may estimate the IQMM parameters for agiven frequency f_(k) directly, for example, by sending single-tonesignals at f_(k) and −f_(k) separately using two differentpre-compensator coefficients and/or settings. The envelope detectoroutputs at frequency 2f_(k) for these measurements may then be combinedand solved using, for example, a quadratic equation in closed form toobtain the frequency-dependent gain and phase mismatches at f_(k). Thenthe IQMM parameters ϕ_(TX) and V_(TX)(f) may be found, for example, assimple functions of the frequency-dependent gain and phase mismatchesfor each frequency f_(k).

Some example implementation details may be as follows. A single-tonesignal at frequencies f_(k) and −f_(k) may be applied separately at BBto a TX path without any IQMC. e.g., W_(TX)[n]=0, for the CVCarchitecture illustrated in FIG. 2 , and the frequency response of theenvelope detector output at frequency 2f_(k) may be denoted by Y_(1,k)and Y_(2,k) respectively. Another set of pre-compensation parametersw[n] with a delay element of T_(D)=0 may be chosen and applied, and asingle-tone signal at frequency f_(k) may be sent. The frequencyresponse of the envelope detector output at frequency 2f_(k) may bedenoted by Y_(3,k). This may result in the following equations

$\begin{matrix}{\mspace{76mu}{{Y_{1,k} = {A_{TX}^{2}{G_{1{TX}}\left( f_{k} \right)}{G_{2{TX}}^{*}\left( {- f_{k}} \right)}}},\mspace{76mu}{Y_{2,k} = {A_{TX}^{2}{G_{1{TX}}^{*}\left( {- f_{k}} \right)}{G_{2{TX}}\left( f_{k} \right)}}},{Y_{3,k} = {\frac{A_{TX}^{2}}{4}\left\lbrack {{{G_{1{TX}}\left( f_{k} \right)}{G_{2{TX}}^{*}\left( {- f_{k}} \right)}J_{1}^{2}} + {{G_{2{TX}}\left( f_{k} \right)}{G_{1{TX}}^{*}\left( {- f_{k}} \right)}J_{2}^{2}} + \left( {{{G_{1{TX}}\left( f_{k} \right)}{G_{1{TX}}^{*}\left( {- f_{k}} \right)}} + {{G_{2{TX}}\left( f_{k} \right)}{G_{2{TX}}^{*}\left( {- f_{k}} \right)}J_{1}J_{2}}} \right\rbrack} \right.}}}} & (11)\end{matrix}$where J₁ and J₂ may be known values that may be defined as followsJ ₁=1,J ₂ =W* _(TX)(−f _(k)).  (12)

Equations (11) may be reformulated using the relationshipV_(TX)(f_(k))=V_(TX)(−f_(k)) and Equations (2) and (3) as

$\begin{matrix}{\mspace{76mu}{{Y_{1,k} = {{\gamma\left( {{V_{TX}\left( f_{k} \right)} + e^{j\;\phi_{TX}}} \right)}\left( {{V_{TX}\left( f_{k} \right)} - e^{{- j}\;\phi_{TX}}} \right)}},\mspace{76mu}{Y_{2,k} = {{\gamma\left( {{V_{TX}\left( f_{k} \right)} + e^{{- j}\;\phi_{TX}}} \right)}\left( {{V_{TX}\left( f_{k} \right)} - e^{j\;\phi_{TX}}} \right)}},{Y_{3,k} = {\frac{\gamma}{4}\left\lbrack {{J_{1}^{2}Y_{1,k}} + {J_{2}^{2}Y_{1,k}} + {\frac{J_{1}J_{2}}{4}\left( {{\left( {{V_{TX}\left( f_{k} \right)} + e^{j\;\phi_{TX}}} \right)\left( {{V_{TX}\left( f_{k} \right)} + e^{{- j}\;\phi_{TX}}} \right)} + {\left( {{V_{TX}\left( f_{k} \right)} - e^{j\;\phi_{TX}}} \right)\left( {{V_{TX}\left( f_{k} \right)} - e^{{- j}\;\phi_{TX}}} \right)}} \right)}} \right\rbrack}},\mspace{76mu}{{{where}\mspace{14mu}\gamma} = {A_{TX}^{2}\text{/}{\left( {4{{gH}_{QTX}(f)}} \right).}}}}} & (13)\end{matrix}$

Equations (13) may provide six real equations with five real unknowns,i.e., Re{γ}, Im{γ}, Re{V_(TX)(f_(k))}, Im{V_(TX)(f_(k))}, ϕ_(TX), whichmay be solved to obtain estimates of V_(TX)(f_(k)) and ϕ_(TX). IQMMparameter V_(TX)(−f_(k)) may be estimated as {circumflex over(V)}_(TX)(−f_(k))={circumflex over (V)}*_(TX)(f_(k)), which may followfrom h_(ITX)(t) and h_(QTX)(t) being real-valued filters that may beconjugate symmetric in the frequency domain. i.e.,H_(ITX)(f)=H*_(ITX)(−f) and H_(QTX)(f)=H*_(QTX)(−f).

Method 3

In some embodiments, this method may involve sending two-tone pilotsignals at frequencies f_(k) ₁ , f_(k) ₂ and −f_(k) ₁ , −f_(k) ₂ andf_(k) ₁ , −f_(k) ₂ separately. The envelope detector outputs for thesemeasurements at frequencies 2f_(k) ₁ , 2f_(k) ₂ , f_(k) ₁ ±f_(k) ₂ maythen be combined and solved in closed form, for example, using twoquadratic equations to obtain estimates of ϕ_(TX) and V_(TX)(f) atf=±f_(k) ₁ , ±f_(k) ₂ directly.

Referring to FIG. 9 , in some embodiments of this method, a two-tonesignal at frequencies f_(k) ₁ , f_(k) ₂ may be generated and sent at TXbaseband, i.e., S(f)=A_(TX) ₁ δ(f−f_(k) ₁ )+A_(TX) ₂ δ(f−f_(k) ₂ ), andthe time-domain signal may be captured at the output of the envelopedetector. The frequency response of the time-domain signal may bedenoted as

Y_(1, k) = R(f)|_(f = 2f_(k₁)), Y_(2, k) = R(f)|_(f = 2f_(k₂)), Y_(3, k) = R(f)|_(f = f_(k₁) + f_(k₂)), Y_(4, k) = R(f)|_(f = f_(k₁) − f_(k₂)).Next, a multi-tone signal may be sent at frequencies f_(k) ₁ and −f_(k)₂ , i.e., S(f)=A_(TX) ₁ δ(f−f_(k) ₁ )+A*_(TX) ₂ δ(f+f_(k) ₂ ), and thefrequency responses of the envelope detector output at frequencies f_(k)₁ ±f_(k) ₂ may be denoted as

Y_(5, k) = R(f)❘_(f = f_(k₁) + f_(k₂))  and  Y_(6, k) = R(f)❘_(f = f_(k₁) − f_(k₂)).Then, a multi-tone signal may be sent at frequencies −f_(k) ₁ and −f_(k)₂ . i.e., S(f)=A*_(TX) ₁ δ(f+f_(k) ₁ )+A*_(TX) ₂ δ(f+f_(k) ₂ ), and thecaptured frequency response of the envelope signal at frequencies f_(k)₁ ±f_(k) ₂ may be denoted as

Y_(7, k) − R(f)❘_(f = f_(k₁) + f_(k₂))  and  Y_(8, k) = R(f)❘_(f = f_(k₁) − f_(k₂)).The following parameters may be defined:

$\begin{matrix}{{x_{1} = {A_{{TX}_{1}}{G_{1{TX}}\left( f_{k_{1}} \right)}}},{x_{2} = {A_{{TX}_{1}}{G_{1{TX}}^{*}\left( {- {f_{k}}_{1}} \right)}}},{y_{1} = {A_{{TX}_{1}}{G_{2{TX}}^{*}\left( {- f_{k_{1}}} \right)}}},{y_{2} = {A_{{TX}_{1}}{G_{2{TX}}\left( f_{k_{1}} \right)}}},{z_{1} = {A_{{TX}_{2}}{G_{1{TX}}\left( f_{k_{2}} \right)}}},{z_{2} = {A_{{TX}_{2}}{G_{1{TX}}^{*}\left( {- f_{k_{2}}} \right)}}},{w_{1} = {A_{{TX}_{2}}{G_{2{TX}}^{*}\left( {- f_{k_{2}}} \right)}}},{w_{2} = {A_{{TX}_{2}}{{G_{2{TX}}\left( f_{k_{2}} \right)}.}}}} & (14)\end{matrix}$

Combining all of the observations may provide the following set ofnon-linear equations:Y _(1,k) =x ₁ y ₁,Y _(2,k) =z ₁ w ₁,Y _(3,k) =x ₁ w ₁ +y ₁ z ₁,Y _(4,k) =x ₁ z* ₁ +y ₁ w* ₁,Y _(5,k) =x ₁ z ₂ +y ₁ w ₂,Y _(6,k) =x ₁ w* ₂ +y ₁ z* ₂,Y _(7,k) =x ₂ w ₂ +y ₂ z ₂,Y _(8,k) =x ₂ z* ₂ +y ₂ w* ₂.  (15)

This set of 8 equations with 8 unknowns in Equations (15) may be solved,for example, using the following steps:

1.

-   -   a. The following parameters may be calculated for l=1, 2 and        i=1, 2

${\beta_{1,l} = \frac{Y_{3,k} + {\left( {- 1} \right)^{l}\sqrt{Y_{3,k}^{2} - {4Y_{1,k}Y_{2,k}}}}}{2}},{\beta_{2,i} = \frac{Y_{4,k} + {\left( {- 1} \right)^{i}\sqrt{Y_{4,k}^{2} - {4Y_{1,k}Y_{2,k}^{*}}}}}{2Y_{2,k}^{2}}}$

-   -   b. {circumflex over (x)}₁, ŷ₁, {circumflex over (z)}₁, and ŵ₁        may be calculated as

${{\hat{x}}_{1} = \sqrt{{\beta_{1,l_{k}}\beta_{2,i_{k}}^{*}}}},{{\hat{w}}_{1} = \frac{\beta_{1,l_{k}}}{{\hat{x}}_{1}}},{{\hat{y}}_{1} = \frac{Y_{1,k}}{{\hat{x}}_{1}}},{{\hat{z}}_{1} = \frac{Y_{2,k}}{{\hat{w}}_{1}}}$

-   -   where

$i_{k} = {{{\underset{i}{argmax}\left( {\beta_{2,i}} \right)}\mspace{14mu}{and}\mspace{14mu} l_{k}} = {\underset{l}{argmin}\left( {{lm}\left\{ {{\beta_{1,l}\beta_{2,i_{k}}^{*}}} \right\}} \right)}}$

-   -   c. {circumflex over (x)}₂, ŷ₂, {circumflex over (z)}₂, and ŵ₂        may be calculated as

${\begin{bmatrix}{\hat{z}}_{2} \\{\hat{w}}_{2}\end{bmatrix} = {\begin{bmatrix}{\hat{x}}_{1} & {\hat{y}}_{1} \\{\hat{y}}_{1}^{*} & {\hat{x}}_{1}^{*}\end{bmatrix}^{- 1}\begin{bmatrix}Y_{5,k} \\Y_{6,k}\end{bmatrix}}},{\begin{bmatrix}{\hat{x}}_{2} \\{\hat{y}}_{2}\end{bmatrix} = {\begin{bmatrix}{\hat{w}}_{2} & {\hat{z}}_{2} \\{\hat{z}}_{2}^{*} & {\hat{w}}_{2}^{*}\end{bmatrix}^{- 1}\begin{bmatrix}Y_{7,k} \\Y_{8,k}\end{bmatrix}}}$

-   -   d. T_(k) _(r) and T_(−k) _(r) may be calculated as

${T_{k_{1}}\overset{\Delta}{=}\frac{{\hat{x}}_{1} + {\hat{y}}_{2}}{{\hat{x}}_{1} - {\hat{y}}_{2}}},{T_{- k_{1}}\overset{\Delta}{=}\frac{{\hat{x}}_{2}^{*} + {\hat{y}}_{1}^{*}}{{\hat{x}}_{2}^{*} - {\hat{y}}_{1}^{*}}},{T_{k_{2}}\overset{\Delta}{=}\frac{{\hat{z}}_{1} + {\hat{w}}_{1}}{{\hat{z}}_{1} - {\hat{w}}_{1}}},{T_{- k_{2}}\overset{\Delta}{=}\frac{{\hat{z}}_{2}^{*} + {\hat{w}}_{1}^{*}}{{\hat{z}}_{2}^{*} - {\hat{w}}_{1}^{*}}}$2. After obtaining all T_(k) ₁ , T_(k) ₂ , T_(−k) ₁ , and T_(−k) ₂ where

${k \in \left\{ {1,\ldots\;,\frac{K}{2}} \right\}},$

-   -   a. ϕ_(TX) may be estimated as

${\hat{\phi}}_{TX} = {\frac{1}{2K}{\sum\limits_{k = 1}^{\frac{K}{2}}\;\left( {{{angle}\left( \frac{T_{- k_{1}}^{*}}{T_{k_{1}}} \right)} + {{angle}\left( \frac{T_{- k_{2}}^{*}}{T_{k_{2}}} \right)}} \right)}}$

-   -   b. Estimates of V_(TX)(f) may be obtained as follows        {circumflex over (V)} _(TX)(f _(k) _(r) )=T _(k) _(r) e        ^(j{circumflex over (ϕ)}) ^(TX) ,{circumflex over (V)} _(TX)(−f        _(k) _(r) )=T _(−k) _(r) e ^(j{circumflex over (ϕ)}) ^(TX) , for        r=1,2,

In some embodiments, f_(k1)>0 and f_(k) ₂ >0 may be chosen such that thefrequencies 2f_(k) ₁ , 2f_(k) ₂ , f_(k) ₁ +f_(k) ₂ , and |f_(k) ₁ −f_(k)₂ | may be distinct.

The selection of two-tone pilot signals (and positive and negativefrequencies thereof), as well as the resulting envelope detector outputsignals selected for analysis are for purposes of illustration only, andother combinations of pilot signals and/or output signals may be used.For example, in the second set of signals in FIG. 9 , −f_(k) ₁ and f_(k)₂ may be used instead of f_(k) ₁ and −f_(k) ₂ . Some unused signals areshown with dotted lines in FIG. 9 , but in other embodiments, thesesignals may be used while others may be unused. Although someembodiments may be described in the context of two-tone pilot signals,pilot signals with any number of tones may be used. e.g., three-tone,four-tone, etc.

As described above, in some embodiments, one or more of the equationsthat may be obtained using method 3 may include one or more IQMMparameters of the two frequencies of a two-tone signal. In contrast, insome embodiments using method 2, each equation may only contain the IQMMof a single-frequency. Thus, in some embodiments, and depending on theimplementation details, different sets of equations may be obtainedusing different methods.

Obtaining IQMC Coefficients

In some embodiments, after obtaining estimates of ϕ_(TX) and V_(TX)(f)for f=±f₁, . . . , ±f_(K), these estimates may be used to compensate forFD-IQMM in the TX path. In some example embodiments, a least squares(LS) method may be implemented as follows: for a given delay elementT_(D), the parameter W_(TX) ^(opt)(f) given in Equation (4) may beestimated at frequencies f=±f₁, . . . , ±f_(K). For example, in anembodiment having a finite impulse response (FIR) filterw_(TX)[n]=Σ_(i=0) ^(L-1)w_(TX,i)δ[n−i] of length L, the method mayobtain the optimal L-tap filter w_(TX)=[w_(TX,0), . . . ,w_(TX,L-1)]^(T)∈

^(L×1) that may minimize the least squared (LS) error between W_(TX)(f)and Ŵ_(TX) ^(opt)(f) at frequencies f=±f₁, . . . , ±f_(K) as

$\begin{matrix}{{\min\limits_{w_{TX},T_{D}}{{{\hat{W}}_{opt} - {Fw}_{TX}}}^{2}},} & (16)\end{matrix}$where Ŵ_(opt)=[Ŵ_(TX) ^(opt)(−f_(K)), . . . , Ŵ_(TX) ^(opt)(−f₁), Ŵ_(TX)^(opt)(f₁), . . . , Ŵ_(TX) ^(opt)(f_(K))]^(T) and F=[F₀, . . . ,F_(L-1)] is the discrete Fourier transform (DFT) matrix of size 2K×L. Insome embodiments, T_(D) may take values in {0, . . . , L−1}. For a fixedT_(D), w_(TX) may be found as ŵ_(TX,T) _(D) =pinv(F)Ŵ_(opt) with a leastsquared error of LSE_(T) _(D) =∥Ŵ_(opt)−Fŵ_(TX,TD)∥². Then the optimalT_(D) and filter coefficients TX may be given by

$\begin{matrix}{{T_{D}^{opt} = {\underset{T_{D}}{argmin}{LSE}_{T_{D}}}},{{\hat{w}}_{TX}^{opt} = {{\hat{w}}_{{TX},T_{D}^{opt}}.}}} & (17)\end{matrix}$

Although some techniques have been described in the context ofpre-compensator structures such as the one illustrated in FIG. 2 , theinventive principles are not limited to these examples, and calibrationalgorithms according to this disclosure may be applied to other IQMCstructures as well. Furthermore, techniques other than LS may be used toobtain filter coefficients for IQMC structures based on estimated IQMMparameters, and the methodologies described here are only examples forillustrating the inventive principles.

In any of the embodiments disclosed herein, frequency domain signals(e.g., signals R_(1,k), . . . , R_(4,k) in FIG. 10 ) may be obtained bycapturing the baseband time-domain signal and converting it to afrequency-domain signal using a fast Fourier transform (FFT) as anexample.

FIG. 10 illustrates an embodiment of method for TX IQMM calibrationusing an RX feedback path according to this disclosure. The methodillustrated in FIG. 10 may be used, for example, with the systemillustrated in FIG. 4 . The method illustrated in FIG. 10 may begin atoperation 1000. At operation 1002, a counter k may be initialized to 1.At operation 1004, the method may check the value of the counter k. If kis less than or equal to the maximum value K, the method may proceed tooperation 1006 where a single-tone pilot signal may be generated atfrequency f_(k) and applied at baseband to the TX path 400. At operation1008, the received pilot signal may be captured at frequencies f_(k) and−f_(k) at baseband of the RX path 402 and denoted by R_(1,k) andR_(2,k), respectively. At operation 1010, a single-tone pilot signal maybe generated at frequency −f_(k) and applied at baseband to the TX path400. At operation 1012, the received pilot signal may be captured atfrequencies −f_(k) and f_(k) at baseband of the RX path 402 and denotedby R_(3,k) and R_(4,k), respectively.

At operation 1014, the method may increment the value of the counter kand return to operation 1004, where the method may check the value ofthe counter k. If k is greater than the maximum value K, the method mayproceed to operation 1016 where, using the observations for R_(1,k), . .. , R_(4,k), ∀k, the method may estimate the IQMM parameters ϕ_(TX) andV_(TX)(f), f=±f₁, . . . , ±f_(K). At operation 1018, the method may useϕ_(TX) and V_(TX)(f), f=±f₁, . . . , ±f_(K) to estimate coefficients forthe TX IQMM pre-compensator 418. The method may then terminate atoperation 1020.

As mentioned above, in some embodiments. R_(1,k), . . . , R_(4,k) may beobtained by capturing the time-domain signal at BB of the RX path 402and converting it to a frequency-domain signal, for example, using anFFT.

FIG. 11 illustrates an embodiment of a first method for TX IQMMcalibration using an envelope detector according to this disclosure. Themethod illustrated in FIG. 11 may be used, for example, with the systemillustrated in FIG. 7 . The method illustrated in FIG. 11 may begin atoperation 1100. At operation 1102, a counter k may be initialized to 1.At operation 1104, the method may check the value of the counter k. If kis less than or equal to the maximum value K, the method may proceed tooperation 1106 where a new pre-compensator setting may be selected frompossible pre-compensator values. At operation 1108, a single-tone pilotsignal may be generated at frequency −f_(k) and applied at baseband tothe TX path 700. At operation 1110, the signal at the output of the ABBfilter in the envelope detector path at frequency 2f_(k) may becaptured. At operation 1112, the method may check the power of thecaptured signal. If the power is a non-negligible value, the method mayreturn to operation 1106. If the power is zero or a negligible value,the method may proceed to operation 1114 where the optimal value for thepre-compensator settings for frequency f_(k) may be set to the currentsettings. At operation 1116, the procedure may be repeated for thesingle-tone signal generated at f_(k).

At operation 1118, the method may increment the value of the counter kand return to operation 1104, where the method may check the value ofthe counter k. If k is greater than the maximum value K, the method mayproceed to operation 1120 where, using the pre-compensation settings for±f₁, . . . , ±f_(k), the method may estimate the IQMM parameters ϕ_(TX)and V_(TX)(f), f=±f₁, . . . , ±f_(K). At operation 1122, the method mayuse ϕ_(TX) and V_(TX)(f), f=±f₁, . . . , ±f_(K) to estimate coefficientsfor the TX IQMM pre-compensator 718. The method may then terminate atoperation 1124.

FIG. 12 illustrates an embodiment of a second method for TX IQMMcalibration using an envelope detector according to this disclosure. Themethod illustrated in FIG. 12 may be used, for example, with the systemillustrated in FIG. 7 . The method illustrated in FIG. 12 may begin atoperation 1200. At operation 1202, a counter k may be initialized to 1.At operation 1204, the method may check the value of the counter k. If kis less than or equal to the maximum value K, the method may proceed tooperation 1206 where a first pre-compensator setting, for example withno IQMC, may be selected. At operation 1208, the method may generate andsend a single-tone signal at frequency f_(k) at the BB of transmit path700. The signal at the output of ABB filter 730 and 732 in the envelopedetector path may be captured at frequency 2f_(k) and denoted asY_(1,K). In some embodiments, the signal may be captured after the ADCs734 and 736. At operation 1210, the method may generate and send asingle-tone signal at frequency −f_(k) at the BB of transmit path 700.The signal at the output of ABB filter 730 and 732 in the envelopedetector path may be captured at frequency 2f_(k) and denoted asY_(2,k). At operation 1212, the method may select a secondpre-compensator setting to apply to the TX path 700. At operation 1214,the method may generate and send a single-tone signal at frequency f_(k)at the BB of transmit path 700. The signal at the output of ABB filter730 and 732 in the envelope detector path may be captured at frequency2f_(k) and denoted as Y_(3,k).

At operation 1216, the method may increment the value of the counter kand return to operation 1204, where the method may check the value ofthe counter k. If k is greater than the maximum value K, the method mayproceed to operation 1218 where, using Y_(1,k), Y_(2,k), and Y_(3,k),for every k, the method may estimate the IQMM parameters ϕ_(TX) andV_(TX)(f), f=±f₁, . . . , ±f_(K). At operation 1220, the method may useϕ_(TX) and V_(TX)(f), f=±f₁, . . . , ±f_(K) to estimate coefficients forthe TX IQMM pre-compensator 718. The method may then terminate atoperation 1222.

FIG. 13 illustrates an embodiment of a third method for TX IQMMcalibration using an envelope detector according to this disclosure. Themethod illustrated in FIG. 13 may be used, for example, with the systemillustrated in FIG. 7 . The method illustrated in FIG. 13 may begin atoperation 1300. At operation 1302, a counter k may be initialized to 1.At operation 1304, the method may check the value of the counter k. If kis less than or equal to the maximum value K, the method may proceed tooperation 1306 where a two-tone signal may be generated and sent atfrequencies f_(k), f_(k) ₂ at baseband of the TX path 700. At operation1308, the signal at the output of ABB filter 730 and 732 in the envelopedetector path may be captured at frequencies 2f_(k) ₁ , 2f_(k) ₂ , f_(k)₁ +f_(k) ₂ , f_(k) ₁ −f_(k) ₂ , and denoted as Y_(1,k), Y_(2,k),Y_(3,k), Y_(4,k), respectively. At operation 1310, a two-tone signal maybe generated and sent at frequencies f_(k) ₁ , −f_(k) ₂ at baseband ofthe TX path 700. At operation 1312, the signal at the output of ABBfilter 730 and 732 in the envelope detector path may be captured atfrequencies f_(k) ₁ +f_(k) ₂ , f_(k) ₁ −f_(k) ₂ , and denoted asY_(5,k), Y_(6,k), respectively. At operation 1314, a two-tone signal maybe generated and sent at frequencies −f_(k) ₁ , −f_(k) ₂ , at basebandof the TX path 700. At operation 1316, the signal at the output of ABBfilter 730 and 732 in the envelope detector path may be captured atfrequencies f_(k) ₁ +f_(k) ₂ , f_(k) ₁ −f_(k) ₂ , and denoted asY_(7,k), Y_(8,k), respectively.

At operation 1318, the method may increment the value of the counter kand return to operation 1304, where the method may check the value ofthe counter k. If k is greater than the maximum value K, the method mayproceed to operation 1320 where, using Y_(1,k), . . . , Y_(8,k), forevery k, the method may estimate the IQMM parameters ϕ_(TX) andV_(TX)(f), f=±f₁, . . . , ±f_(K). At operation 1322, the method may useϕ_(TX) and V_(TX)(f), f=±f₁, . . . , ±f_(K) to estimate coefficients forthe TX IQMM pre-compensator 718. The method may then terminate atoperation 1324.

FIG. 14 illustrates an embodiment of a method of pre-compensating fortransmitter IQMM according to this disclosure. The method may begin atoperation 1400. At operation 1402, the method may send a signal throughan up-converter of a transmit path to provide an up-converted signal. Atoperation 1404, the method may determine the up-converted signal througha down-converter of a receive feedback path. At operation 1406, themethod may determine one or more IQMM parameters for the transmit pathbased on the determined up-converted signal, and at operation 1408, themethod may determine one or more pre-compensation parameters for thetransmit path based on the one or more IQMM parameters for the transmitpath. The method may end at operation 1410.

FIG. 15 illustrates another embodiment of a method of pre-compensatingfor transmitter IQMM according to this disclosure. The method may beginat operation 1500. At operation 1502, the method may send a signalthrough an up-converter of a transmit path to provide an up-convertedsignal. At operation 1504, the method may determine the up-convertedsignal through an envelope detector. At operation 1506, the method maydetermine one or more IQMM parameters for the transmit path based on thedetermined up-converted signal, and at operation 1508, the method maydetermine one or more pre-compensation parameters for the transmit pathbased on the one or more IQMM parameters for the transmit path. Themethod may end at operation 1510.

The operations and/or components described with respect to theembodiments illustrated in FIGS. 14 and 15 , as well as any otherembodiments described herein, are example operations and/or components.In some embodiments, some operations and/or components may be omittedand/or other operations and/or components may be included. Moreover, insome embodiments, the temporal and/or spatial order of the operationsand/or components may be varied.

This disclosure encompasses numerous inventive principles relating toassociation and authentication for multi access point coordination.These principles may have independent utility and may be embodiedindividually, and not every embodiment may utilize every principle.Moreover, the principles may also be embodied in various combinations,some of which may amplify the benefits of the individual principles in asynergistic manner.

The embodiments disclosed above have been described in the context ofvarious implementation details, but the principles of this disclosureare not limited to these or any other specific details. For example,some functionality has been described as being implemented by certaincomponents, but in other embodiments, the functionality may bedistributed between different systems and components in differentlocations and having various user interfaces. Certain embodiments havebeen described as having specific processes, steps, etc., but theseterms also encompass embodiments in which a specific process, step, etc.may be implemented with multiple processes, steps, etc., or in whichmultiple process, steps, etc. may be integrated into a single process,step, etc. A reference to a component or element may refer to only aportion of the component or element.

The use of terms such as “first” and “second” in this disclosure and theclaims may only be for purposes of distinguishing the things they modifyand may not indicate any spatial or temporal order unless apparentotherwise from context. A reference to a first thing may not imply theexistence of a second thing. Various organizational aids such as sectionheadings and the like may be provided as a convenience, but the subjectmatter arranged according to these aids and the principles of thisdisclosure are not limited by these organizational aids.

The various details and embodiments described above may be combined toproduce additional embodiments according to the inventive principles ofthis patent disclosure. Since the inventive principles of this patentdisclosure may be modified in arrangement and detail without departingfrom the inventive concepts, such changes and modifications areconsidered to fall within the scope of the following claims.

The invention claimed is:
 1. A method of pre-compensating fortransmitter in-phase (I) and quadrature (Q) mismatch (IQMM), the methodcomprising: sending a first signal through a transmit path to provide asecond signal; sending the second signal through an envelope detector;determining one or more IQMM parameters for the transmit path based onan output of the envelope detector; and determining one or morepre-compensation parameters for the transmit path based on the one ormore IQMM parameters for the transmit path; wherein determining the oneor more IQMM parameters for the transmit path comprises: applying afirst pre-compensation parameter to the transmit path; determining afirst power of a component of the second signal caused by transmit IQMMthrough the envelope detector based on the first pre-compensationparameter; applying a second pre-compensation parameter to the transmitpath; determining a second power of a component of the second signalcaused by transmit IQMM through the envelope detector based on thesecond pre-compensation parameter; and selecting one of the firstpre-compensation parameter or the second pre-compensation parameterbased on a lower of the first power and the second power.
 2. The methodof claim 1, wherein: the method further comprises: applying one or moreadditional pre-compensation parameters to the transmit path; anddetermining one or more additional powers of one or more components ofthe second signal caused by transmit IQMM through the envelope detectorbased on the one or more additional pre-compensation parameters; anddetermining the one or more IQMM parameters for the transmit pathcomprises selecting one of the first pre-compensation parameter, thesecond pre-compensation parameter or the one or more additionalpre-compensation parameters based on a lower of the first power, thesecond power, or the one or more additional powers.
 3. A method ofpre-compensating for transmitter in-phase (I) and quadrature (Q)mismatch (IQMM), the method comprising: sending a first signal through atransmit path to provide a second signal; sending the second signalthrough an envelope detector; determining one or more IQMM parametersfor the transmit path based on an output of the envelope detector; anddetermining one or more pre-compensation parameters for the transmitpath based on the one or more IQMM parameters for the transmit path;wherein determining the one or more IQMM parameters for the transmitpath comprises: applying a first pre-compensation parameter to thetransmit path; determining a first power of a component of the secondsignal caused by transmit IQMM through the envelope detector based onthe first pre-compensation parameter; applying a second pre-compensationparameter to the transmit path; and determining a second power of acomponent of the second signal caused by transmit IQMM through theenvelope detector based on the second pre-compensation parameter; themethod further comprising: sweeping a frequency of the first signal sentthrough the transmit path to provide one or more additional secondsignals; sending the one or more additional second signals through theenvelope detector to provide one or more additional outputs of theenvelope detector; and determining the one or more IQMM parameters forthe transmit path based on the one or more additional outputs of theenvelope detector.
 4. A method of pre-compensating for transmitterin-phase (I) and quadrature (Q) mismatch (IQMM), the method comprising:sending a first input signal at a first frequency through a transmitpath to provide a first output signal; sending a second input signal ata second frequency through the transmit path to provide a second outputsignal; sending the first output signal through an envelope detector toprovide a first output of the envelope detector; sending the secondoutput signal through the envelope detector to provide a second outputof the envelope detector; determining one or more IQMM parameters forthe transmit path based on the first output of the envelope detector andthe second output of the envelope detector; and determining one or morepre-compensation parameters for the transmit path based on the one ormore IQMM parameters for the transmit path.
 5. The method of claim 4,further comprising applying first and second pre-compensation parametersto the transmit path for each of the first and second input signals. 6.The method of claim 5, wherein: determining the one or more IQMMparameters for the transmit path comprises solving a system of equationsbased on the first and second output signals; and a first one of theequations comprises a function, at least in part, of the first andsecond pre-compensation parameters.
 7. The method of claim 5, whereinthe second frequency is a negative of the first frequency at baseband.8. The method of claim 5, further comprising: sweeping the first andsecond frequencies for each of the first and second pre-compensationparameters; determining additional first and second output signals basedon sweeping the first and second frequencies; and determining the one ormore IQMM parameters for the transmit path over frequency based on thedetermined additional first and second output signals.